Unsupervised detection of decoupled subspaces: many-body scars and beyond

TL;DR

This paper presents a quantum machine learning approach using a Quantum Variational Autoencoder to automatically detect and analyze quantum many-body scar states and decoupled subspaces in complex quantum systems.

Contribution

It introduces a novel QVAE-based method for identifying scar states and decoupled subspaces, extending detection beyond known families and applicable to disordered systems.

Findings

Detected new families of quantum scars in the PXP model.

Identified dynamically decoupled subspaces in spin ladder models.

Demonstrated automatic detection of scar states and subspaces.

Abstract

Highly excited eigenstates of quantum many-body systems are typically featureless thermal states. Some systems, however, possess a small number of special, low-entanglement eigenstates known as quantum scars. We introduce a quantum-inspired machine learning platform based on a Quantum Variational Autoencoder (QVAE) that detects families of scar states in spectra of many-body systems. Unlike a classical autoencoder, QVAE performs a parametrized unitary operation, allowing us to compress a single eigenstate into a smaller number of qubits. We demonstrate that the autoencoder trained on a scar state is able to detect the whole family of scar states sharing common features with the input state. We identify families of quantum many-body scars in the PXP model beyond the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ families and find dynamically decoupled subspaces in the Hilbert space of disordered, interacting spin ladder model. The possibility of an automatic detection of subspaces of scar states opens new pathways in studies of models with a weak breakdown of ergodicity and fragmented Hilbert spaces.